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<tr class="t-nv-h2"><td colspan="5"> 双曲函数</td></tr>
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<table class="t-dcl-begin"><tbody>
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<td> <div>定义于头文件 <code>&lt;complex.h&gt;</code>
 </div></td>
<td></td>
<td></td>
</tr>
<tr class="t-dcl t-since-c99">
<td> <div><span class="mw-geshi c source-c"><span class="kw4">float</span> <a href="complex.html"><span class="kw743">complex</span></a>       cacoshf<span class="br0">(</span> <span class="kw4">float</span> <a href="complex.html"><span class="kw743">complex</span></a> z <span class="br0">)</span><span class="sy4">;</span></span></div></td>
<td> (1) </td>
<td> <span class="t-mark-rev t-since-c99">(C99 起)</span> </td>
</tr>
<tr class="t-dcl t-since-c99">
<td> <div><span class="mw-geshi c source-c"><span class="kw4">double</span> <a href="complex.html"><span class="kw743">complex</span></a>      cacosh<span class="br0">(</span> <span class="kw4">double</span> <a href="complex.html"><span class="kw743">complex</span></a> z <span class="br0">)</span><span class="sy4">;</span></span></div></td>
<td> (2) </td>
<td> <span class="t-mark-rev t-since-c99">(C99 起)</span> </td>
</tr>
<tr class="t-dcl t-since-c99">
<td> <div><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span> <a href="complex.html"><span class="kw743">complex</span></a> cacoshl<span class="br0">(</span> <span class="kw4">long</span> <span class="kw4">double</span> <a href="complex.html"><span class="kw743">complex</span></a> z <span class="br0">)</span><span class="sy4">;</span></span></div></td>
<td> (3) </td>
<td> <span class="t-mark-rev t-since-c99">(C99 起)</span> </td>
</tr>
<tr class="t-dsc-header">
<td> <div>定义于头文件 <code>&lt;tgmath.h&gt;</code>
 </div></td>
<td></td>
<td></td>
</tr>
<tr class="t-dcl t-since-c99">
<td> <div><span class="mw-geshi c source-c"><span class="co2">#define acosh( z )</span></span></div></td>
<td> (4) </td>
<td> <span class="t-mark-rev t-since-c99">(C99 起)</span> </td>
</tr>
<tr class="t-dcl-sep"><td></td><td></td><td></td></tr>
</tbody></table>
<div class="t-li1"><span class="t-li">1-3)</span> 计算复数值 <code>z</code> 的复反双曲余弦，分支切割在沿实轴小于 1 的值上。</div>
<div class="t-li1"><span class="t-li">4)</span> 泛型宏：若 <code>z</code> 拥有 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">long</span> <span class="kw4">double</span> <a href="complex.html"><span class="kw743">complex</span></a></span></span> 类型，则调用 <code>cacoshl</code> 。若 <code>z</code> 拥有 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">double</span> <a href="complex.html"><span class="kw743">complex</span></a></span></span> 类型，则调用 <code>cacosh</code> 。若 <code>z</code> 拥有 <span class="t-c"><span class="mw-geshi c source-c"><span class="kw4">float</span> <a href="complex.html"><span class="kw743">complex</span></a></span></span> 类型，则调用 <code>cacoshf</code> 。若 <code>z</code> 为实数或整数，则宏调用对应的实函数（ <span class="t-c"><span class="mw-geshi c source-c">acoshf</span></span> 、 <span class="t-c"><span class="mw-geshi c source-c"><a href="../math/acosh.html"><span class="kw680">acosh</span></a></span></span> 、 <span class="t-c"><span class="mw-geshi c source-c">acoshl</span></span> ）。若 <code>z</code> 为虚数，则宏调用对应的复数版本，而返回类型为复数。</div>
<h3><span class="mw-headline" id=".E5.8F.82.E6.95.B0">参数</span></h3>
<table class="t-par-begin">


<tr class="t-par">
<td>  z
</td>
<td> -
</td>
<td> 复参数
</td></tr></table>
<h3><span class="mw-headline" id=".E8.BF.94.E5.9B.9E.E5.80.BC">返回值</span></h3>
<p><code>z</code> 的复反双曲余弦，沿实轴在区间 <span class="texhtml" style="white-space: nowrap;">[0; ∞)</span> 中，而沿虚轴在区间 <span class="texhtml" style="white-space: nowrap;">[−iπ; +iπ]</span> 中。
</p>
<h3><span class="mw-headline" id=".E9.94.99.E8.AF.AF.E5.A4.84.E7.90.86.E5.8F.8A.E7.89.B9.E6.AE.8A.E5.80.BC">错误处理及特殊值</span></h3>
<p>报告的错误与 <a href="../math/math_errhandling.html" title="c/numeric/math/math errhandling">math_errhandling</a> 一致。
</p><p>若实现支持 IEEE 浮点算术，则
</p>
<ul><li> <span class="t-c"><span class="mw-geshi c source-c">cacosh<span class="br0">(</span><a href="conj.html"><span class="kw760">conj</span></a><span class="br0">(</span>z<span class="br0">)</span><span class="br0">)</span> <span class="sy1">==</span> <a href="conj.html"><span class="kw760">conj</span></a><span class="br0">(</span>cacosh<span class="br0">(</span>z<span class="br0">)</span><span class="br0">)</span></span></span>
</li><li> 若 <code>z</code> 为 <code>±0+0i</code> ，则结果为 <code>+0+iπ/2</code>
</li><li> 若 <code>z</code> 为 <code>+x+∞i</code> （对于任何有限 x ），则结果为 <code>+∞+iπ/2</code>
</li><li> 若 <code>z</code> 为 <code>+x+NaNi</code> （对于任何非零有限 x ），结果为 <code>NaN+NaNi</code> 并可能引发 <span class="t-lc"><a href="../fenv/FE_exceptions.html" title="c/numeric/fenv/FE exceptions">FE_INVALID</a></span>
</li><li> 若 <code>z</code> 为 <code>0+NaNi</code> ，则结果为 <code>NaN±iπ/2</code> ，其中虚部符号未指定
</li><li> 若 <code>z</code> 为 <code>-∞+yi</code> （对于任何有限正 y ），则结果为 <code>+∞+iπ</code>
</li><li> 若 <code>z</code> 为 <code>+∞+yi</code> （对于任何有限正 y ），则结果为 <code>+∞+0i</code>
</li><li> 若 <code>z</code> 为 <code>-∞+∞i</code> ，则结果为 <code>+∞+3iπ/4</code>
</li><li> 若 <code>z</code> 为 <code>±∞+NaNi</code> ，则结果为 <code>+∞+NaNi</code>
</li><li> 若 <code>z</code> 为 <code>NaN+yi</code> （对于任何有限 y ），则结果为 <code>NaN+NaNi</code> 并可能引发 <span class="t-lc"><a href="../fenv/FE_exceptions.html" title="c/numeric/fenv/FE exceptions">FE_INVALID</a></span> 。
</li><li> 若 <code>z</code> 为 <code>NaN+∞i</code> ，则结果为 <code>+∞+NaNi</code>
</li><li> 若 <code>z</code> 为 <code>NaN+NaNi</code> ，则结果为 <code>NaN+NaNi</code>
</li></ul>
<h3><span class="mw-headline" id=".E6.B3.A8.E6.84.8F">注意</span></h3>
<p>尽管 C 标准命名此函数为“复弧双曲余弦”，双曲函数的反函数是面积函数。其参数为双曲扇形的面积，而非弧长。正确名称是“复反双曲余弦”，和更少见的“复面积双曲余弦”。
</p><p>反双曲余弦是多值函数，在复平面上要求分支切割。约定将分支切割置于实轴的线段 <span class="texhtml" style="white-space: nowrap;">(-∞,+1)</span> 上。
</p><p>复反双曲余弦主值的数学定义是 <span class="texhtml" style="white-space: nowrap;">acosh z = ln(z + <span class="t-mrad"><span>√</span><span>z+1</span></span> <span class="t-mrad"><span>√</span><span>z-1</span></span>)</span> 。
</p>
对于任何 z ， <span class="texhtml" style="white-space: nowrap;">acosh(z) = <span class="t-mfrac"><table><tr><td><span class="t-mrad"><span>√</span><span>z-1</span></span></td></tr><tr><td><span class="t-mrad"><span>√</span><span>1-z</span></span></td></tr></table></span> acos(z)</span> ，或在复平面上半部简单地为 <span class="texhtml" style="white-space: nowrap;">i acos(z)</span> 。
<h3><span class="mw-headline" id=".E7.A4.BA.E4.BE.8B">示例</span></h3>
<div class="t-example"><div class="t-example-live-link"><div class="coliru-btn coliru-btn-run-init">运行此代码</div></div>
<div dir="ltr" class="mw-geshi" style="text-align: left;"><div class="c source-c"><pre class="de1"><span class="co2">#include &lt;stdio.h&gt;</span>
<span class="co2">#include &lt;complex.h&gt;</span>
 
<span class="kw4">int</span> main<span class="br0">(</span><span class="kw4">void</span><span class="br0">)</span>
<span class="br0">{</span>
    <span class="kw4">double</span> <a href="complex.html"><span class="kw743">complex</span></a> z <span class="sy1">=</span> cacosh<span class="br0">(</span><span class="nu16">0.5</span><span class="br0">)</span><span class="sy4">;</span>
    <a href="../../io/fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"cacosh(+0.5+0i) = %f%+fi<span class="es1">\n</span>"</span>, <a href="creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z<span class="br0">)</span>, <a href="cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
 
    <span class="kw4">double</span> <a href="complex.html"><span class="kw743">complex</span></a> z2 <span class="sy1">=</span> <a href="conj.html"><span class="kw760">conj</span></a><span class="br0">(</span><span class="nu16">0.5</span><span class="br0">)</span><span class="sy4">;</span> <span class="co1">// 或 C11 中的 cacosh(CMPLX(0.5, -0.0))</span>
    <a href="../../io/fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"cacosh(+0.5-0i) (the other side of the cut) = %f%+fi<span class="es1">\n</span>"</span>, <a href="creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z2<span class="br0">)</span>, <a href="cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z2<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
 
    <span class="co1">// 在上半平面， acosh(z) = i*acos(z) </span>
    <span class="kw4">double</span> <a href="complex.html"><span class="kw743">complex</span></a> z3 <span class="sy1">=</span> <a href="casinh.html"><span class="kw799">casinh</span></a><span class="br0">(</span><span class="nu0">1</span><span class="sy2">+</span>I<span class="br0">)</span><span class="sy4">;</span>
    <a href="../../io/fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"casinh(1+1i) = %f%+fi<span class="es1">\n</span>"</span>, <a href="creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z3<span class="br0">)</span>, <a href="cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z3<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
    <span class="kw4">double</span> <a href="complex.html"><span class="kw743">complex</span></a> z4 <span class="sy1">=</span> I<span class="sy2">*</span><a href="casin.html"><span class="kw784">casin</span></a><span class="br0">(</span><span class="nu0">1</span><span class="sy2">+</span>I<span class="br0">)</span><span class="sy4">;</span>
    <a href="../../io/fprintf.html"><span class="kw848">printf</span></a><span class="br0">(</span><span class="st0">"I*asin(1+1i) = %f%+fi<span class="es1">\n</span>"</span>, <a href="creal.html"><span class="kw754">creal</span></a><span class="br0">(</span>z4<span class="br0">)</span>, <a href="cimag.html"><span class="kw751">cimag</span></a><span class="br0">(</span>z4<span class="br0">)</span><span class="br0">)</span><span class="sy4">;</span>
<span class="br0">}</span></pre></div></div>
<p>输出：
</p>
<div dir="ltr" class="mw-geshi" style="text-align: left;"><div class="text source-text"><pre class="de1">cacosh(+0.5+0i) = 0.000000-1.047198i
cacosh(+0.5-0i) (the other side of the cut) = 0.500000-0.000000i
casinh(1+1i) = 1.061275+0.666239i
I*asin(1+1i) = -1.061275+0.666239i</pre></div></div> 
</div>
<h3><span class="mw-headline" id=".E5.BC.95.E7.94.A8">引用</span></h3>
<div class="t-ref-std-11">
<ul><li> C11 standard (ISO/IEC 9899:2011): 
</li></ul>
<dl><dd><ul><li> 7.3.6.1 The cacosh functions (p: 192)
</li></ul>
</dd></dl>
<dl><dd><ul><li> 7.25 Type-generic math &lt;tgmath.h&gt; (p: 373-375)
</li></ul>
</dd></dl>
<dl><dd><ul><li> G.6.2.1 The cacosh functions (p: 539-540)
</li></ul>
</dd></dl>
<dl><dd><ul><li> G.7 Type-generic math &lt;tgmath.h&gt; (p: 545)
</li></ul>
</dd></dl>
<div class="t-ref-std-c99">
<ul><li> C99 standard (ISO/IEC 9899:1999): 
</li></ul>
<dl><dd><ul><li> 7.3.6.1 The cacosh functions (p: 174)
</li></ul>
</dd></dl>
<dl><dd><ul><li> 7.22 Type-generic math &lt;tgmath.h&gt; (p: 335-337)
</li></ul>
</dd></dl>
<dl><dd><ul><li> G.6.2.1 The cacosh functions (p: 474-475)
</li></ul>
</dd></dl>
<dl><dd><ul><li> G.7 Type-generic math &lt;tgmath.h&gt; (p: 480)
</li></ul>
</dd></dl>
</div>
<h3><span class="mw-headline" id=".E5.8F.82.E9.98.85">参阅</span></h3>
<table class="t-dsc-begin">

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="cacos.html" title="c/numeric/complex/cacos"> <span class="t-lines"><span>cacos</span><span>cacosf</span><span>cacosl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td>  计算复数反余弦 <br> <span class="t-mark">(函数)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="casinh.html" title="c/numeric/complex/casinh"> <span class="t-lines"><span>casinh</span><span>casinhf</span><span>casinhl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td>  计算复数反双曲正弦 <br> <span class="t-mark">(函数)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="catanh.html" title="c/numeric/complex/catanh"> <span class="t-lines"><span>catanh</span><span>catanhf</span><span>catanhl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td>  计算复数反双曲正切 <br> <span class="t-mark">(函数)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="ccosh.html" title="c/numeric/complex/ccosh"> <span class="t-lines"><span>ccosh</span><span>ccoshf</span><span>ccoshl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td>  计算复双曲余弦 <br> <span class="t-mark">(函数)</span> </td></tr>

<tr class="t-dsc">
<td>  <div class="t-dsc-member-div"><div><a href="../math/acosh.html" title="c/numeric/math/acosh"> <span class="t-lines"><span>acosh</span><span>acoshf</span><span>acoshl</span></span></a></div><div><span class="t-lines"><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span><span><span class="t-mark-rev t-since-c99">(C99)</span></span></span></div></div>
</td>
<td>   计算反双曲余弦（ <span class="mjax" style="display:none">\({\small\operatorname{arcosh}{x} }\)</span><span class="mjax-fallback texhtml" style="white-space: nowrap;">arcosh(x)</span> ）  <br> <span class="t-mark">(函数)</span> </td></tr>

</table></div>

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